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<p>This work extends the analysis of a class of evolutionary history-dependent variational-hemivariational inequalities, introduced in [Migórski, S., Dudek, S.: A class of evolutionary history-dependent variational–hemivariational inequalities with strong and weak solutions, SeMA Journal 82(2), 179–203 (2025)], by focusing on their optimal control. After briefly recalling the main theoretical results, we prove the continuous dependence of solutions on the problem data. Subsequently, we formulate an optimal control problem and prove the existence of optimal controls. Finally, the abstract framework is illustrated by a dynamic frictional contact problem, where the material behavior is modeled by a viscoelastic constitutive law with long-memory and the contact conditions are described by a generalized Signorini-type unilateral boundary condition involving a nonmonotone Clarke subdifferential relation.</p>

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Optimal control of a class of evolutionary history-dependent variational–hemivariational inequalities with application in Contact mechanics

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • Ouaanabi Abdelhafid,
  • Alaoui Mohammed,
  • Bouallala Mustapha,
  • Essoufi El Hassan

摘要

This work extends the analysis of a class of evolutionary history-dependent variational-hemivariational inequalities, introduced in [Migórski, S., Dudek, S.: A class of evolutionary history-dependent variational–hemivariational inequalities with strong and weak solutions, SeMA Journal 82(2), 179–203 (2025)], by focusing on their optimal control. After briefly recalling the main theoretical results, we prove the continuous dependence of solutions on the problem data. Subsequently, we formulate an optimal control problem and prove the existence of optimal controls. Finally, the abstract framework is illustrated by a dynamic frictional contact problem, where the material behavior is modeled by a viscoelastic constitutive law with long-memory and the contact conditions are described by a generalized Signorini-type unilateral boundary condition involving a nonmonotone Clarke subdifferential relation.